partial fraction problem

Question

I have thought for a long time but general method is not working :

$$\frac{s^2+2}{(s+2)^2(s^2+2s+2)^2}$$

Thanks for all help.

Answer 1

Hint:

$$\frac{s^2+2}{(s+2)^2(s^2+2s+2)^2} = \frac{As+B}{(s+2)^2}+ \frac{Cs^3+Ds^2+Es+F}{(s^2+2s+2)^2}$$